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Cube Rotation

Tool to list the possible positions of a cube. A die is a cube with 6 differentiated faces, it can be defined by its visible faces so as to know its possible orientations / rotations.

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Cube Rotation -

Tag(s) : Fun/Miscellaneous

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# Cube Rotation

## Dice Rotations

### How to list all rotations of the cube?

Place the cube on one side and orient it according to the 4 directions. Move to the next position (other side) and so on to get all rotations.

Example:

 - 1 - 5 4 2 - 6 - - 3 -

### How to count all possible rotations of a cube?

The die can fall on one of the 6 faces possible and be oriented according to 4 angles, or 24 possibilities. $$6 \times 4 = 24$$

### Mathematically, how rotations of a cube are defined?

There are 4 types of rotation of a dice:

— Rotation according to the diagonals

— Rotation along the axis connecting the centers of 2 opposite faces

— Rotation along the axis connecting the centers of 2 opposite edges

— Identity rotation (original stationary state)

### How to count all possible symmetries of a cube?

A cube whose faces are undifferentiated with 13 axes of symmetries:

— 3 axes pass through the centers of the faces, a cube has 6 faces, so 3 axes

— 6 axes pass through the centers of the opposite edges, a cube has 12 edges, so 6 axes

— 4 axes go through the opposite corners, a cube has 8 angles, so 4 axes

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Cube Rotation on dCode.fr [online website], retrieved on 2023-01-29, https://www.dcode.fr/cube-rotation

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